A sequential ADMM algorithm to find sparse LCP solutions using a l2−l1 regularization technique with …

The linear complementary problem (LCP) is a unified formulation for linear and quadratic programming problems. Therefore, it has many applications in practical problems like bimatrix game. We prove that it makes sense to look for sparse LCP solutions. A l2−l1 regularization technique transforms the original sparse optimization problem into an unconstrained one. Thereafter, a linearized ADMM (for alternating direction method of multipliers) is designed to solve the regularization model. Then, using a penalty function approach, we propose an efficient sequential linearized ADMM to find the sparse LCP solutions. Finally, numerical experiments prove that the sparse solution of LCPs can be solved efficiently, and is competitive with other state-of-the-art algorithms. A practical application in bimatrix game is also reported.